We do strange things to ourselves in the process of acquiring culture with a capital K. We get ourselves to believe that there are twelve tones in the octave and are so surprised that composers come up with twenty-three (see Allan Kozzin's article in yesterday's New York Times). There are actually millions of tones out of which different cultures choose a manageable number to which they pitch their songs and their instruments. When western composers write well for the traditional orchestra they are releasing many more tones than those in the notated score: all them overtones!

And the piano? It was always a microtonal instrument and it still is. Only our insistence on those twelve keys keeps us from hearing that.

I had a great row with a quite prominent musician/teacher/authority on the subject. He was aghast at the notion. Then why, I ask, did Brahms routinely account for 21 tones in the octave, and Schubert 24 in his posthumous B-flat Sonata?

The keys are not the sound.

Let's think about speed: I think it's fair to say that Beethoven developed the notion of musical speed more explicitly than anyone else, specifically the direct connection between the very fast and the very slow. I am convinced that he responded to the vibration speed in slow tempos, of which most of us are entirely unaware.

One of my students is incredibly aware of that speed and, oddly, it slows down his superficial motor responses. It is an internal involvement which has required of me that I learn to hear and respect it. This is the student who plays a Beethoven sound more expressively than I can imagine doing myself. I am convinced that he responds to the piano in a manner comparable to Beethoven's, otherwise he could not intuitively find such a sound.

The sound defies theoretical identification or description much the way that piano sound defies electronic synthesis.

Playing painlessly is like holding your nose when you swallow something you expect to taste awful. But what if you are holding your nose all the time?

The best image for playing painlessly remains Milt Gross's brilliant solution to King Midas breaking his teeth when he chewed his peas: He had a vassal stand in the corner with a pea shooter to shoot the peas directly into his gullet so that he could swallow them without chewing them.

If you do an Internet search for Nize Baby you will find some lovely peas on which to chew.

Few things are more revealing than a Beethoven Sonata in the hands of a teenage student: I see in her comprehension-motivated reading the exact opposite of my reading at her age (16), the goal of which was to play it as painlessly as possible.

This morning I discovered that one movement that has always felt weird to me need not feel weird at all: it begins with an upbeat bar while I had always heard it as a downbeat bar which, of course, throws the entire movement off balance. She got it; I did not.

A real dilemma faces educators now more than ever: Do we train children to answer or to ask questions? If to answer, then we assume that the questions we are asking are relevant to our children. If to ask, we assume that we are all living in a changing world and that the teacher generation has no idea what the questions of their era will be.

Those who favor answers are currently setting the tone of public education in this country.

I favor questions.

One of my students has the ear of a composer. When he doesn't approve of the note choices of a composer whose work he is reading he changes the notes without thinking about it.

As he is a visual arts student I asked if he had ever copied a painting. Yes. Well, every time you play this piece you are copying the composition; your errors are not acceptable if the job is to copy the work as it is, not as you would prefer it to be. Playing a piece on the piano can seem like a repetitive activity unless approached with a fully awakened sense of responsibility.

An eminent scholar referred in a study on Mozart to the way amateurs massacre certain of his works. I don't think it's their fault. I blame the instrument teachers who cannot distinguish between music that is technically easy to play and music that is profoundly transparent. I am thinking of those "easy" Mozart sonatas and of Schumann's Fantasy Pieces--given routinely to intermediate level clarinetists and cellists, though they are among the most sophisticated ensemble duo that exist. Once you give people a taste of incompetence for which they receive praise the ship is already sinking.